Between the legs of the rod linkage forming the folding system, such folding tops for passenger cars have a flexible roofing which, in the folded-back position in the rear region of the passenger car, is covered together with the rod linkage of the top with a canvas or other cover as a protective enclosure. Mounting such a protective enclosure represents a necessary measure which is associated with a corresponding effort, since driving without an enclosure represents a source of danger during a possible collision. Moreover, a folding top, which is not protected, becomes dirty more quickly.